The space of convex domains in complex Euclidean space

In this mostly expository article, we describe some properties of the space of convex domains in complex Euclidean space (endowed with the local Hausdorff topology). In particular, we give careful proofs that the Kobayashi metric, the Bergman kernel/metric, and the Kähler–Einstein metric are all con...

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Veröffentlicht in:The Journal of geometric analysis Jg. 30; H. 2; S. 1312 - 1358
Hauptverfasser: Gaussier, Hervé, Zimmer, Andrew
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.04.2020
Springer Nature B.V
Springer
Schlagworte:
Abstract Harmonic Analysis
an Important Tool in Several Complex Variables
Automorphisms
Closures
Convex and Discrete Geometry
Differential Geometry
Domains
Dynamical Systems and Ergodic Theory
Euclidean geometry
Euclidean space
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Invariant Metrics
Mathematics
Mathematics and Statistics
Topology
Invariant metrics and pseudodistances
Convex domains
32F17
Primary 32F45
ISSN:1050-6926, 1559-002X
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:In this mostly expository article, we describe some properties of the space of convex domains in complex Euclidean space (endowed with the local Hausdorff topology). In particular, we give careful proofs that the Kobayashi metric, the Bergman kernel/metric, and the Kähler–Einstein metric are all continuous on the space of convex domains. The group of affine automorphisms acts on this space and we also describe the orbit closures for some special classes of domains.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-019-00346-5